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# Calculate The Surface Area of A Paraboloid

Last updated: Saturday, April 29, 2023

A paraboloid is a 3 dimensional surface that's obtained by the revolution of a parabola around its axis. The surface area of a paraboloid is the total area of the curved surface of a 3D object that has the shape of a parabola. The formula for the surface area of a paraboloid depends on its specific form, whether it is a circular paraboloid or an elliptical paraboloid.

In real-life applications, paraboloids are commonly used in reflectors such as parabolic antennas, telescopes, and satellite dishes. The surface area of a paraboloid is important to determine the amount of material required to construct these objects.

Calculating the surface area of a paraboloid involves integrating a mathematical function, which can be complex. As such, it is often simpler to use numerical methods or software to calculate the surface area.

The formula for determining the surface area of paraboloid is defined as:
$$SA$$ $$=$$ $$\dfrac{\pi \cdot a}{6 \cdot h^2}$$ $$\cdot$$ $$\big((a^2 + 4 \cdot h^2)^{3/2} - a^3\big)$$
$$SA$$: the surface area of the paraboloid
$$a$$: the radius of the paraboloid base
$$h$$: the height of the paraboloid
$$\pi$$: A mathematical constant with an infinite decimal tail
The SI unit of surface area is: $$square \text{ } meter\text{ }(m^2)$$

## Find $$SA$$

Use this calculator to determine the surface area of a paraboloid given the radius and height
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the radius of the paraboloid base
$$a$$
$$meter$$
the height of the paraboloid
$$h$$
$$meter$$
$$\pi$$ : A mathematical constant with an infinite decimal tail
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